1. Field of the Invention
This invention relates to analysis of vibration in a transmission belt. More particularly, the invention is directed to a method, an apparatus, and a program for performing the vibration analysis using a vibration analysis model.
2. Background Art
It is known to perform vibration analysis for a power transmission system utilizing a vibration analysis model. The vibration analysis may facilitate system design that accounts for a long operating life for the transmission belt, taking into account load, belt tension, number of pulley revolutions, belt velocity, diameter of the pulleys, layout of pulleys, and the like.
One exemplary, conventional, vibration analysis method is disclosed in JP-A-2001-311456. In this system, a belt on a pulley is divided into nodes of relatively minute length. The nodes are coupled with elastic elements or rigid elements. The vibration analysis is conducted by observing the belt and pulley as they come into contact with, and separate from, each other. Likewise, with the vibration analysis model, the belt element is divided into nodes of relatively minute length.
In the above conventional vibration analysis method, using a vibration analysis model, compression distortion may cause the arithmetic calculation of a simulated span tension to be negative, i.e. in a compressed state. However, given that a transmission belt is a pliant, continuous beam, and the fact that experimentation shows that the belt between spans is maintained in an elliptical state, it is not possible for an actual span of the belt to have a negative tension. Thus, in the vibration analysis model, using this conventional vibration analysis method, the span tension is determined by calculating using a spring constant reduced to or fixed at zero, or is determined by making calculations with a spring element removed. However, this determination is carried out in the abstract, with there being no concrete basis for making a correction in this manner.
Another vibration analysis method is disclosed in JP-A-2001-311456. A belt element is divided into nodes of minute length. In this particular method, the vibration analysis model is quite complicated. Generation of a program to perform the arithmetic calculations to conduct the analysis may be complicated and potentially time consuming.
In one form, the invention is directed to a method of analyzing vibration in a longitudinal direction of a transmission belt that is trained around at least a drive pulley and a driven pulley in a power transmission system. The method includes the steps of using a vibration analysis model which involves: a) generating data relative to the power transmission system; and b) calculating belt tension values, including a selected belt tension value, using the generated data. In the event that the selected belt tension value is calculated to be at or lower than a predetermined belt tension value, a correction is made in the selected belt tension value. The corrected, selected, calculated belt tension value is used to carry out the vibration analysis.
The step of using a vibration analysis model may involve modeling belt portions between each of the drive and the driven pulleys, and a pulley adjacent to each of the drive and driven pulleys, using a Voigt model to calculate a belt tension value to be used with the Voigt model from a formula including an harmonic function simulating revolutions of a crankshaft for the drive pulley.
The step of making a correction may involve making a correction using an expression of a curvilinear relation which does not become zero.
In one form, the step of making a correction involves making a correction using an expression of a curvilinear relation associated by an exponential function.
The step of making a correction may involve making a correction using the following expression:
Txe2x80x2=Tspxc3x97exp ((T/Tsp)xe2x88x921)
where: T is the selected calculated belt tension value;
Tsp is the predetermined belt tension value; and
Txe2x80x2 is the corrected selected calculated belt tension value.
The step of calculating the selected belt tension value may involve calculating the selected belt tension value in a belt portion in which there is compression distortion.
The invention is further directed to an apparatus for analyzing vibration in a longitudinal direction of a transmission belt that is trained around at least a drive pulley and a driven pulley in a power transmission system. The apparatus includes a first structure for receiving data relative to the power transmission system and, through the data, preparing a vibration analysis using a vibration analysis model. The first structure is capable of calculating belt tension values, including a selected belt tension value. The first structure is further capable of making a correction in the selected calculated belt tension value used in preparing the vibration analysis in the event that the selected calculated belt tension value is at or lower than the predetermined belt tension value.
The first structure may be capable of modeling belt portions between each of the drive and driven pulleys, and a pulley adjacent to each of the drive and driving pulleys, using a Voigt model to calculate a belt tension value, to be used with the Voigt model, from a formula including an harmonic function simulating revolution of a crankshaft for the drive pulley.
The first structure may be capable of making a correction using an expression of a curvilinear relation which does not become zero.
The correction may be made using an expression of a curvilinear relation associated by an exponential function.
The correction may be made by using the following expression.
Txe2x80x2Tspxc3x97exp ((T/Tsp)xe2x88x921)
where: T is the calculated selected belt tension value;
Tsp is the predetermined belt tension value; and
Txe2x80x2 is the corrected calculated selected belt tension value.
In one form, the first structure is capable of calculating the selected belt tension value at a belt portion at which there is compression distortion.
The invention is further directed to a program for use with a computer to permit analysis of vibration in a longitudinal direction of a transmission belt that is trained around at least a drive pulley and a driven pulley in a power transmission system. The program, when loaded in a computer, causes the computer to process data relative to the power transmission system and thereby prepare a vibration analysis using a vibration analysis model. The program causes the computer to calculate belt tension values including a selected belt tension value and further to make a correction in the selected calculated belt tension value used in preparing the vibration analysis in the event that the selected calculated belt tension value is at or lower than a predetermined belt tension value.
The program may cause the computer to model belt portions between each of the drive and driven pulleys and a pulley adjacent to each of the drive and driven pulleys using a Voigt model to calculate a belt tension value to be applied to the Voigt model from a formula including an harmonic function simulating revolution of a crankshaft for the drive pulley.
The program may cause the computer to make a correction using an expression of a curvilinear relation which does not become zero.
The program may cause the computer to make a correction using an expression of a curvilinear relation associated by an exponential function.
The program may cause the computer to make a correction using the following expression.
xe2x80x83Txe2x80x2=Tspxc3x97exp ((T/Tsp)xe2x88x921)
where: T is the selected calculated belt tension value;
Tsp is the predetermined belt tension value; and
Txe2x80x2 is the corrected calculated selected belt tension value.
The program may cause the computer to calculate the selected belt tension value at a belt portion at which there is compression distortion.
The program may be provided in combination with a computer into which the program is loaded.